Mathematics

# The value of $\displaystyle\lim_{x\rightarrow 0}\dfrac{\displaystyle\int^{x^2}_0\cos t^2dt}{x\sin x}$ is?

$3/2$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

Q1 Subjective Medium
$\displaystyle \int{1\over {\sin x{{\cos }^3}x}}dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
The value of $\displaystyle \int_{0}^{\pi /2}\sin \theta \log \left ( \sin \theta \right )\:d\theta$ equals
• A. $\displaystyle \log_{e}\left ( \frac{1}{e} \right )$
• B. $\displaystyle \log _{2}e$
• C. $\displaystyle \log_{e}\left ( \frac{e}{2} \right )$
• D. $\displaystyle \log_{e}{2}-1$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Solve :
$\int e^x \left( log x + \dfrac {1}{x^2} \right) dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Hard
Solve:
$\displaystyle \int_{0}^{1} \sqrt {\dfrac {1-x}{1+x}dx}$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
Evaluate $\displaystyle \int \dfrac{x^{2}}{(a^{6}-x^{6})}dx$
• A. $\dfrac{1}{6a^{3}} \log\left | \dfrac{a^{3}-x^{3}}{a^{3}+x^{3}} \right |+C$
• B. $\dfrac{1}{6a^{3}} \log\left | \dfrac{2a^{3}}{a^{3}-x^{3}} \right |+C$
• C. none of these
• D. $\dfrac{1}{6a^{3}}\log\left | \dfrac{a^{3}+x^{3}}{a^{3}-x^{3}} \right |+C$